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Broad Topics > Handling, Processing and Representing Data > Averages

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Statistical Shorts

Stage: 3 and 4 Challenge Level: Challenge Level:1

Can you decide whether these short statistical statements are always, sometimes or never true?

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How Would You Score It?

Stage: 3 Challenge Level: Challenge Level:1

Invent a scoring system for a 'guess the weight' competition.

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For Richer for Poorer

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Charlie has moved between countries and the average income of both has increased. How can this be so?

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Searching for Mean(ing)

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?

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M, M and M

Stage: 3 Challenge Level: Challenge Level:1

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

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The Monte Carlo Method

Stage: 5 Challenge Level: Challenge Level:1

Estimate areas using random grids

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Match the Matches

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Decide which charts and graphs represent the number of goals two football teams scored in fifteen matches.

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Litov's Mean Value Theorem

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

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Unequal Averages

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Play around with sets of five numbers and see what you can discover about different types of average...

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Half a Minute

Stage: 3 Challenge Level: Challenge Level:1

Anna, Ben and Charlie have been estimating 30 seconds. Who is the best?

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Wipeout

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Can you do a little mathematical detective work to figure out which number has been wiped out?

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About Average

Stage: 3 Challenge Level: Challenge Level:1

Can you find sets of numbers which satisfy each of our mean, median, mode and range conditions?

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May the Best Person Win

Stage: 1, 2, 3 and 4

How can people be divided into groups fairly for events in the Paralympics, for school sports days, or for subject sets?

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David and Goliath

Stage: 4 and 5 Challenge Level: Challenge Level:1

Does weight confer an advantage to shot putters?

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PDF

Stage: 5 Challenge Level: Challenge Level:1

Given a probability density function find the mean, median and mode of the distribution.

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Top Coach

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.

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Spread

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Given the mean and standard deviation of a set of marks, what is the greatest number of candidates who could have scored 100%?

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Bat Wings

Stage: 3 Challenge Level: Challenge Level:1

Three students had collected some data on the wingspan of some bats. Unfortunately, each student had lost one measurement. Can you find the missing information?